{"ID":2847735,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00183","arxiv_id":"2511.00183","title":"PDE-SHARP: PDE Solver Hybrids through Analysis and Refinement Passes","abstract":"Current LLM-driven approaches using test-time computing to generate PDE solvers execute a large number of solver samples to identify high-accuracy solvers. These paradigms are especially costly for complex PDEs requiring substantial computational resources for numerical evaluation. We introduce PDE-SHARP, a framework to reduce computational costs by replacing expensive scientific computation by cheaper LLM inference that achieves superior solver accuracy with 60-75% fewer computational evaluations. PDE-SHARP employs three stages: (1) Analysis: mathematical chain-of-thought analysis including PDE classification, solution type detection, and stability analysis; (2) Genesis: solver generation based on mathematical insights from the previous stage; and (3) Synthesis: collaborative selection-hybridization tournaments in which LLM judges iteratively refine implementations through flexible performance feedback. To generate high-quality solvers, PDE-SHARP requires fewer than 13 solver evaluations on average compared to 30+ for baseline methods, improving accuracy uniformly across tested PDEs by $4\\times$ on average, and demonstrates robust performance across LLM architectures, from general-purpose to specialized reasoning models.","short_abstract":"Current LLM-driven approaches using test-time computing to generate PDE solvers execute a large number of solver samples to identify high-accuracy solvers. These paradigms are especially costly for complex PDEs requiring substantial computational resources for numerical evaluation. We introduce PDE-SHARP, a framework t...","url_abs":"https://arxiv.org/abs/2511.00183","url_pdf":"https://arxiv.org/pdf/2511.00183v2","authors":"[\"Shaghayegh Fazliani\",\"Madeleine Udell\"]","published":"2025-10-31T18:38:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Large Language Model\"]","has_code":false}